Abstract: This paper proves that Sage Husa′s adaptive Kalman filtering algorithm cannot estimate Q and R simultaneously, and analyses the reason why Sage Husa′s algorithm may lead to filtering divergence. A new algorithm of adaptive Kalman filter is introduced which can estimate Q (or R) accurately when R (or Q)is known. The most particular feature of this algorithm is that only matrix multiplication and inversion are performed while no summation or reduction is carried out in the phase of updating and improving the estimation of Q(or R), hence resulting in no filtering divergence. Digital simulation shows that it is remarkable.

Key words: adaptiv e filtering, inertial nav ig atio n, integ rat ed navigat ion